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Blockchains are currently gaining attention as a newly emerging technology in both academia and industry, capable of impacting a variety of domains beyond cryptocurrencies. Performance modeling can be used to provide us with a deeper understanding of the behavior and dynamics within blockchain peer-to-peer networks. Blockchain system architects can leverage network models to properly tune their system and to reduce design costs significantly. In this article, we focus on the original and well-established Bitcoin blockchain network. In particular, we propose a random graph model for performance modeling and analysis of the inventory-based protocol for block dissemination. This model addresses the impact of key blockchain parameters on the overall performance of Bitcoin. We derive some explicit and closed-form equations for block propagation delay and traffic overhead in the Bitcoin network. We also adapt our model to study the impact of deploying a relay network and investigate the effect of the relay network size on the network performance and decentralization. We implement our model using the popular network simulator OMNet++. We validate the accuracy of our theoretical model and its implementation with our dataset mined from the Bitcoin network. Our results show the tradeoff between the default number of connections per node, network bandwidth, and block size in order to compute the optimal block propagation delay over the network. Additionally, we found that bigger relay networks can jeopardize the decentralization of the Bitcoin network. [ABSTRACT FROM AUTHOR]